Physical review. B, Condensed matter

Unrestricted Hartree-Fock upper bounds for the total energy of the Hubbard model on a Bethe lattice of infinite connectivity

J. Galán, José Antonio Vergés

Published Nov 1, 1994• 0 citations

Abstract

An unrestricted Hartree-Fock (UHF) scheme is used to obtain approximate solutions of the Hubbard model on a Bethe lattice of infinite connectivity. The UHF energy yields a correct upper bound of the total energy over the whole phase diagram. In addition to the disappearance of antiferromagnetic long-range order away from half-filling, our results give a line separating the magnetic region of the phase diagram from the nonmagnetic one.

DOI: 10.1103/physrevb.50.13817

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Physical review. B, Condensed matter

Unrestricted Hartree-Fock upper bounds for the total energy of the Hubbard model on a Bethe lattice of infinite connectivity

J. Galán, José Antonio Vergés

Published Nov 1, 1994• 0 citations

Publisher

Abstract

DOI: 10.1103/physrevb.50.13817

Related papers

Phase diagram of the half-filled extended Hubbard model in two dimensions

Biplab Chattopadhyay, D. M. Gaitonde

We consider an extended Hubbard model of interacting fermions on a lattice. The fermion kinetic energy corresponds to a tight-binding Hamiltonian with nearest-neighbor (-t) and next-nearest-neighbor ( ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$ ) hopping matrix elements. In addition to the on-site Hubbard interaction (U) we also consider a nearest-neighbor repulsion (V). We obtain the zero-temperature phase diagram of our model within the Hartree-Fock approximation. We consider ground states having charge- and spin-density-wave ordering as well as states with orbital antiferromagnetism or spin nematic order. The latter two states correspond to particle-hole binding with ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ symmetry in the charge and spin channels, respectively. For ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$ =0, only the charge-density-wave and spin-density-wave states are energetically stable. For nonzero ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$ , we find that orbital antiferromagnetism (or spin nematic) order is stable over a finite portion of the phase diagram at weak coupling. This region of stability is seen to grow with increasing values of ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$ .We consider an extended Hubbard model of interacting fermions on a lattice. The fermion kinetic energy corresponds to a tight-binding Hamiltonian with nearest-neighbor (-t) and next-nearest-neighbor (${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$) hopping matrix elements. In addition to the on-site Hubbard interaction (U) we also consider a nearest-neighbor repulsion (V). We obtain the zero-temperature phase diagram of our model within the Hartree-Fock approximation. We consider ground states having charge- and spin-density-wave ordering as well as states with orbital antiferromagnetism or spin nematic order. The latter two states correspond to particle-hole binding with ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ symmetry in the charge and spin channels, respectively. For ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$=0, only the charge-density-wave and spin-density-wave states are energetically stable. For nonzero ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$, we find that orbital antiferromagnetism (or spin nematic) order is stable over a finite portion of the phase diagram at weak coupling. This region of stability is seen to grow with increasing values of ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$.

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Physical review. B, Condensed matterJul 1, 199310 citations

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M. YU, Hua Lin

In this paper, we study phase separation in the two-dimensional single-band Hubbard model with the unrestricted Hartree-Fock(UHF) method and the restricted Hartree-Fock (RHF) method. We perform the calculation for square lattices and rectangle lattices. It is observed that the stripe phase exists and it depends on three aspects: geometry of the lattice, Coulomb interaction U and band filling n. To gain more physical insights, we consider the Hubbard model with spin dependent hoppings: t↑ and t↓, and study the effect of varying [Formula: see text] on the phase separation.In this paper, we study phase separation in the two-dimensional single-band Hubbard model with the unrestricted Hartree-Fock(UHF) method and the restricted Hartree-Fock (RHF) method. We perform the calculation for square lattices and rectangle lattices. It is observed that the stripe phase exists and it depends on three aspects: geometry of the lattice, Coulomb interaction U and band filling n. To gain more physical insights, we consider the Hubbard model with spin dependent hoppings: t↑ and t↓, and study the effect of varying [Formula: see text] on the phase separation.

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The Hartree-Fock ground-state phase diagram of the one-dimensional Hubbard model is calculated in the $μ-U$ plane, restricted to phases with no charge density modulation, extending the results presented in cond-mat/9511116. This allows antiferromagnetism, saturated ferromagnetism, spiral spin density waves and a collinear structure with unit cell $\uparrow \uparrow \downarrow \downarrow$ . The spiral phase is unstable against phase separation near quarter-, half- and three-quarter-filling. For large $U$ this occurs at hole (or electron) doping of $(3t/π^{2}U)^{1/3}$ from half filling.The Hartree-Fock ground-state phase diagram of the one-dimensional Hubbard model is calculated in the $μ-U$ plane, restricted to phases with no charge density modulation, extending the results presented in cond-mat/9511116. This allows antiferromagnetism, saturated ferromagnetism, spiral spin density waves and a collinear structure with unit cell $\uparrow \uparrow \downarrow \downarrow$. The spiral phase is unstable against phase separation near quarter-, half- and three-quarter-filling. For large $U$ this occurs at hole (or electron) doping of $(3t/π^{2}U)^{1/3}$ from half filling.

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Determination of the Hubbard model parameters by using the unrestricted Hartree–Fock solutions, and improvement of their energies

Daisuke Yamaki, Koji Yasuda, Kizashi Yamaguchi

Abstract A strategy is proposed to determine parameters in model Hamiltonians from the difference of the density matrices calculated by ab initio methods. As an example, the parameters of the two‐site Hubbard model are determined. The parameters t and U are explicitly expressed in terms of the energy difference and the difference of the expectation values of the spin operator 〈S2〉 between two unrestricted Hartree–Fock (UHF) solutions. By using this relation and the exact energy formulas of the model Hamiltonian the energies of the ground and excited states of the ab initio Hamiltonian are estimated. This energy estimation scheme is applied to H2 and Li2 molecules and the results are in reasonable agreement with those of the full configuration‐interaction method. The errors of our estimation are also discussed and evaluated by using a modified Hubbard model. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005Abstract A strategy is proposed to determine parameters in model Hamiltonians from the difference of the density matrices calculated by ab initio methods. As an example, the parameters of the two‐site Hubbard model are determined. The parameters t and U are explicitly expressed in terms of the energy difference and the difference of the expectation values of the spin operator 〈S2〉 between two unrestricted Hartree–Fock (UHF) solutions. By using this relation and the exact energy formulas of the model Hamiltonian the energies of the ground and excited states of the ab initio Hamiltonian are estimated. This energy estimation scheme is applied to H2 and Li2 molecules and the results are in reasonable agreement with those of the full configuration‐interaction method. The errors of our estimation are also discussed and evaluated by using a modified Hubbard model. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

International Journal of Quantum ChemistryJan 1, 20050 citations

{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}

) hopping matrix elements. In addition to the on-site Hubbard interaction (U) we also consider a nearest-neighbor repulsion (V). We obtain the zero-temperature phase diagram of our model within the Hartree-Fock approximation. We consider ground states having charge- and spin-density-wave ordering as well as states with orbital antiferromagnetism or spin nematic order. The latter two states correspond to particle-hole binding with ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ symmetry in the charge and spin channels, respectively. For

{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}

=0, only the charge-density-wave and spin-density-wave states are energetically stable. For nonzero

{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}

, we find that orbital antiferromagnetism (or spin nematic) order is stable over a finite portion of the phase diagram at weak coupling. This region of stability is seen to grow with increasing values of

{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}

The Hartree-Fock ground-state phase diagram of the one-dimensional Hubbard model is calculated in the

μ-U

plane, restricted to phases with no charge density modulation, extending the results presented in cond-mat/9511116. This allows antiferromagnetism, saturated ferromagnetism, spiral spin density waves and a collinear structure with unit cell

\uparrow \uparrow \downarrow \downarrow

. The spiral phase is unstable against phase separation near quarter-, half- and three-quarter-filling. For large

U

this occurs at hole (or electron) doping of

(3t/π^{2}U)^{1/3}

from half filling.